Nanofiber embedded bioinspired strong wet friction surface

Robust and reversible wet attachments are important for medical engineering and wearable electronics. Although ultrastrong capillarity from interfacial nano-thick liquid bridges creates tree frog’s strong wet friction, its unstable nano-liquid characteristic challenges further wet friction enhancement. Here, unique hierarchical micro-nano fibrous pillars have been discovered on Chinese bush crickets exhibiting a robust wet friction ~3.8 times higher than tree frog’s bulk pillar. By introducing a nano-fibrous pillar array covered with thin films (NFPF), the pillar’s separation position switches from the rear to front side compared with bulk pillars, indicating the interfacial contact stress shifting from compressing to stretching. This largely decreases the interfacial separation stress to form more stable and larger nano-liquid bridges. The NFPF array with self-splitting of interfacial liquid and contact stress further guards such interfacial stress shifting to ensure a ~1.9 times friction enhancement. Last, the theories are established, and the applications on wearable electronics are validated.


The PDF file includes:
Supplementary Texts A to C Figs. S1 to S16 Table S1 Other Supplementary Material for this manuscript includes the following:

Movies S1 to S5
Supplementary Text A. On BP, the relationship between the solid contact stress, capillary pressure, and external lateral force Due to the homogeneous structure of the BP, the BP is deformed and inclined under the bending moment formed by the lateral force FLB and pillar height h (Fig. 4A).The force balance between capillary pressure PCap and solid-solid contact stress distribution function P(x) in the normal direction of the contact interface can be represented as where d and L refer to the width and thickness of the pillar, respectively.Selecting corner A as the pivot point, the bending moment equilibrium formed by solid-solid contact stress P(x), external lateral force FLB, and capillary pressure PCap can be expressed as With the increase of lateral force, the contact stress PF at pillar front side increases, while the stress PR at pillar rear side decreases.When PR drops to zero, the pillar starts to separate from the substrate along with reaching the maximum friction.Then the maximum lateral force FLB-max can be derived as It is noted that the maximum lateral force FLB-max decreases with the increase of the pillar height h, suggesting that a high pillar height will weaken the frictional properties of the pillar surface, which is in agreement with the experimental results.
B. On NFPF, the relationship between the solid contact stress, capillary pressure, and external lateral force To establish the theoretical model of NFPF stress transmission, the bioinspired pillar surface is divided into the upper surface and lower fiber array (Fig. 4C), which have a linear relationship between the force and deformation, similar to elastic springs.
Based on the linear relationship between the axial tensile deformation and the axial tension of the fiber, the fiber can be considered as an elastic spring with an equivalent elasticity coefficient of  .Define  ,  as the axial strain and axial tension of the nth fiber, respectively.The axial tension of the nth fiber  can be presented as    ℎ where  ∆ℎ ℎ ⁄ in which ∆ℎ denotes the nth fiber axial elongation.Define  as the horizontal tilting angle of the nth fiber.According to the geometric relationship shown in the diagram (Fig. 4C),   and   can be represented as The force balance at the contact interface in horizontal direction (Fig. 4C) can be expressed as By simplifying the strain variation from the 1st to the Nth fiber as a linear change, then equation S5 can be expressed as where     ⁄ , in which  is the diameter of the fiber, and w refers to the spacing between fibers.When the pillar front end starts to detach from the substrate and slide, the pillar surface reaches its highest friction with maximum lateral force FLF-max.At this point, the normal force balance at the contact interface for the most anterior fiber, i.e., the Nth fiber, can be represented as     * , i.e., where Pcap is the capillary pressure and L is the thickness of the pillar.
Based on the force equilibrium at the upper surface, the maximum lateral force FLF-max and the elongation  of the upper surface have a relation of  ∆  S8 where  represents the equivalent elasticity coefficient of the upper surface.According to the geometric relationship shown in the diagram (Fig. 4C), ∆ can be represented as ∆ ℎ   2 ℎ   2 where  and  denote the strain of the Nth and 1st fiber, respectively.Then equation S8 can be rewritten as  ℎ   2 ℎ   2  S9 Combining equations S6, S7 and S9, the maximum lateral force FLF-max can be derived as where  ℎ/,  /.As the fiber height increases, the maximum lateral force FLF-max becomes larger, indicating that bioinspired pillars with high fiber arrays feature greater frictional properties.

C. Comparison of the theoretical maximum friction between the NFPF surface and the BP surface
To compare the theoretical frictional performance of the NFPF and BP,  is defined as the ratio between the maximum friction on the NFPF and BP, i.e., the ratio of the maximum lateral force on the NFPF (FLF-max) to that on the BP (FLB-max).where E represents the elastic modulus of the fiber.For numerical calculations, the elastic modulus E of PDMS is taken to be 1 MPa, and Pcap is assumed to be the capillary pressure of a 200 nm thick liquid film, about 700 kPa.The structural parameters of bioinspired surfaces are listed as below Table S1.Characterization of the liquid film behavior on the Chinese bush cricket pad in friction.

Movie S2.
Characterization of the liquid film behavior and structural deformation on BP in friction.

Movie S3.
Characterization of the liquid film behavior and structural deformation on NFPF in friction.

Movie S4.
Characterization of the liquid film behavior and structural deformation on PSAN in friction.

Movie S5.
Flowing water resistance test for smooth and bioinspired surface patches.

Fig. S1 .
Fig. S1.Internal structural characteristics of the Chinese bush cricket attachment pads.(A, B) SEM for the Chinese bush cricket attachment pad after critical point drying.(C, D) Cryo-SEM for frozen fractured biological sample.

Fig. S2 .
Fig. S2.Characterization of the effective elastic modulus of the Chinese bush cricket attachment pad.The indentation of the pad versus applied force.The red line is the indentation data fitted according to the Hertz model theory.The indentation of the pad was calculated by subtracting the displacement of the hard surface from the displacement of the pad at the same spring deflection to obtain the indentation of the pad under the force corresponding to that deflection.The Hertz theory predicts the indentation on the pad under an external force Fn to be     , where R is the average radius of curvature of the pad.The effective elastic modulus K of ~15 kPa for the pad was found by fitting the data for the indentation curve.

Fig. S3 .
Fig. S3.In-situ characterization setup of interfacial liquid film movement and pillar deformation during the friction test.(A) Schematic illustration of performing successive friction tests for attachment pads and observing the dynamic behavior of mucus.(B) Schematic illustration of observing the deformation of micropillars during friction tests for bioinspired surfaces.

Fig. S5 .
Fig. S5.In-situ characterization setup of normal adhesion tests for different surfaces and interfacial liquid film movement on NFPF surface during the separation process.(A) Schematic illustration of performing normal adhesion tests for bioinspired surfaces and observing the dynamic behavior of liquid film.(B) The successive normal adhesion stress of NFPF surface.(C) The maximum adhesion stress of different surfaces.

Fig. S7 .
Fig. S7.In-situ characterization of interfacial liquid film behaviors on BP during the evaporation process and the influence of pillar material properties on the shear stress of BP surfaces.(A) Schematic illustration of observing interfacial liquid film on bioinspired surfaces during the evaporation process.(B) Characterization of pillar deformation induced by liquid bridge on soft and hard pillar surfaces during the interfacial liquid evaporation.(C) The wet friction performance of bioinspired BP surfaces fabricated with various materials.(D) The boundary friction of bioinspired BP surfaces with different water contact angles on various substrates.(E) The boundary friction of bioinspired NFPF-30 surfaces during 20 times friction tests.

Fig. S9 .
Fig. S9.The wet friction performance of bioinspired NFPF surfaces with different fiber heights.(A) Boundary frictional shear stress for NFPF surfaces with different fiber heights.(B) SEM images of NFPFs with the fiber height of 50 μm.(C) Schematic diagram of distinct deformation modes of NFPFs with different aspect ratios.

Fig. S10 .
Fig. S10.The boundary shear stress of the Chinese bush cricket pad on different roughness substrates.All friction tests are measured with a normal load of ~1 kPa and a contact area of ~1 mm 2 .

Fig. S11 .
Fig. S11.SEM images of NFPF-30 with different pillar diameters and their friction performance on various roughness substrates during the boundary friction.(A, B, C) SEM images of NFPF-30 with pillar diameters of 100, 150, and 200 μm, respectively.(D) The shear stress of these NFPF-30 surfaces on substrates with various roughness in the boundary friction.

Fig. S12 .
Fig. S12.Schematic diagram of setting up the finite element analysis (FEA) model and simulation results.(A) The FEA model for BP.(B) The FEA model for NFPF.(C) The contact stress distribution throughout the contact interface of different pillars.(D) The stress tensor distribution at the contact interface of different pillars.

Fig. S13 .
Fig. S13.Theoretical and experimental results of the ratio of the maximum lateral force on the NFPF to that on the BP.The ratio  of theoretical predictions and experimental measurements for bioinspired NFPF surfaces and BP surfaces in different heights.

Fig. S14 .
Fig. S14.FEA simulation for bioinspired pillar array surfaces sliding on a substrate with a different number of pillars.(A) FEA setup for bioinspired BP array surfaces.(B) FEA setup for bioinspired NFPF array surfaces.The lateral displacement is applied at one side of the bioinspired surface, and the downward static pressure is applied on each pillar to simulate the capillary pressure.A friction pair is set between the interface.

Fig. S15 .
Fig. S15.Test equipment setup for bioinspired wearable flexible sensors.The electrical signals generated by the pulse vibration are processed by a charger amplifier and a digital lowpass filter, then displayed by an oscilloscope.Different volumes of water are added to the skin surface with a pipette to simulate different states of sweating.

Fig. S16 .
Fig. S16.The peeling process of bioinspired NFPF patch on volunteer's forearm.This bioinspired NFPF patch can be easily peeled off from the skin, and cause no pain to the skin like vacuum suckers or tissue adhesives do.
Combining equations S4 and S10, leads to Define ℎ as the height of the upper surface, according to the relationship  ε of the upper surface, i.e., According to the stress-strain relationship of the fiber  ε, i.e.,